Fixed computation of density for full matsub mesh

-> Previously, calculation was implicitly assuming a mesh with only positive matsubara frequencies.
-> Added corresponding test
-> Also added test of density calculation with or without correct tail.

test/triqs/gfs/gf_notail.cpp

@@ -42,8 +42,13 @@ int main() {
   TEST(Gt(.9));
   TEST(Gt(-.1));//should be equal to line above
 
-
-
+  //fourier
+   triqs::gfs::local::tail t(1,1);
+  gw_n (tau_) << 1/(tau_-1.);
+  auto gt_with_full_tail = make_gf_from_inverse_fourier(make_gf_from_g_and_tail(gw_n, gw.singularity()));
+  auto gt_tail_with_one_term = make_gf_from_inverse_fourier(make_gf_from_g_and_tail(gw_n, t));
+  TEST(gt_with_full_tail(.5));
+  TEST(gt_tail_with_one_term(.5));
  }
  TRIQS_CATCH_AND_ABORT;
 }

test/triqs/gfs/gf_notail.output

@@ -6,3 +6,15 @@
 
 (Gt(-.1)) ---> -0.40657
 
+(gt_with_full_tail(.5)) ---> ((0.5 * 
+[[-0.44347,0]
+ [0,-0.44347]]) + (0.5 * 
+[[-0.443038,0]
+ [0,-0.443038]]))
+
+(gt_tail_with_one_term(.5)) ---> ((0.5 * 
+[[-0.44347,0]
+ [0,-0.44347]]) + (0.5 * 
+[[-0.443038,0]
+ [0,-0.443038]]))
+

test/triqs/gfs/gf_positive_and_negative_matsubara.cpp

@@ -0,0 +1,33 @@
+//#define TRIQS_ARRAYS_ENFORCE_BOUNDCHECK
+#include <triqs/gfs.hpp> 
+#include <triqs/gfs/local/functions.hpp> 
+using namespace triqs::gfs;
+#define TEST(X) std::cout << BOOST_PP_STRINGIZE((X)) << " ---> "<< (X) <<std::endl<<std::endl;
+
+int main() {
+ try { 
+  double beta =1;int n_im_freq=400;
+  auto G =  gf<imfreq, scalar_valued> {{beta, Fermion, n_im_freq,false}};
+  auto G_pos_only =  gf<imfreq, scalar_valued> {{beta, Fermion, n_im_freq,true}};
+
+  TEST(G.mesh().positive_only());
+  TEST(G_pos_only.mesh().positive_only());
+  //std::cout << G.singularity() << std::endl ;
+  triqs::clef::placeholder<0> om_;
+  G(om_) << 1/(om_ + 2.3);
+  G_pos_only(om_) << 1/(om_ + 2.3);
+
+  auto n = triqs::gfs::density(G);
+  auto n_pos_only = triqs::gfs::density(G_pos_only);
+  TEST(n);
+  TEST(n_pos_only);
+
+  // test hdf5 
+  //H5::H5File file("gf_scalar.h5", H5F_ACC_TRUNC);
+  //h5_write(file, "g", G);
+  //h5_write(file, "gm", reinterpret_scalar_valued_gf_as_matrix_valued(G));
+
+ }
+TRIQS_CATCH_AND_ABORT;
+
+}

test/triqs/gfs/gf_positive_and_negative_matsubara.output

@@ -0,0 +1,10 @@
+(G.mesh().positive_only()) ---> 0
+
+(G_pos_only.mesh().positive_only()) ---> 1
+
+0
+1
+(n) ---> 0.908877
+
+(n_pos_only) ---> 0.908877
+

test/triqs/gfs/gfv2.output

@@ -157,7 +157,8 @@
  [(0,0),(0.151719,-0.207234)]]
 
 -----------------   4 --------------------
-(density(G3)) ---> 
+(density(G3)) ---> 1
+
 [[1.81775,0]
  [0,1.81775]]
 

triqs/gfs/local/functions.cpp

@@ -53,10 +53,10 @@ namespace triqs { namespace gfs {
     //dens_part(n1,n2) = dens_part(n1,n2)*(fact/Beta)  + (d + F(a1,b1,Beta) + F(a2,b2,Beta)+ F(a3,b3,Beta));
     //if (!Green_Function_Are_Complex_in_time) dens_part  = 0+real(dens_part);
    }
-
+  
   for (size_t n1=0; n1<N1;n1++) 
    for (size_t n2=0; n2<N2;n2++) {
-    dens_part(n1,n2) = dens_part(n1,n2) + real(dens_part(n2,n1)) - I * imag(dens_part(n2,n1)) + dens_tail(n1,n2);
+    dens_part(n1,n2) = dens_part(n1,n2) + (G.mesh().positive_only()? ( real(dens_part(n2,n1)) - I * imag(dens_part(n2,n1)) ) : 0) + dens_tail(n1,n2);
     // ?? STRANGE ??
     dens_part(n2,n1) = real(dens_part(n1,n2)) - I * imag(dens_part(n1,n2));
    }